Problem: Solve for $x$ : $5\sqrt{x} - 1 = 9\sqrt{x} + 6$
Explanation: Subtract $5\sqrt{x}$ from both sides: $(5\sqrt{x} - 1) - 5\sqrt{x} = (9\sqrt{x} + 6) - 5\sqrt{x}$ $-1 = 4\sqrt{x} + 6$ Subtract $6$ from both sides: $-1 - 6 = (4\sqrt{x} + 6) - 6$ $-7 = 4\sqrt{x}$ Divide both sides by $4$ $\frac{-7}{4} = \frac{4\sqrt{x}}{4}$ Simplify. $-\dfrac{7}{4} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.